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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Sara is an avid lottery player. In the certain game... tagged by: BTGmoderatorLU ##### This topic has 1 expert reply and 0 member replies ### Top Member ## Sara is an avid lottery player. In the certain game... Sara is an avid lottery player. In the certain game she plays, she must pick one number between 30 and 39, inclusive, one number between 40 and 49, inclusive, and one number between 50 and 59, inclusive. She believes that she will have the best chance of winning if her three numbers, as a set, has the greatest number of distinct prime factors possible. According to Sara's theory, which of the following sets of three numbers should she use? A. 32 - 48 - 52 B. 33 - 42 - 56 C. 39 - 40 - 54 D. 38 - 49 - 51 E. 36 - 42 - 56 The OA is D. I'm really confused with this PS question. Experts, any suggestion about how can I solve it? Thanks in advance. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Top Reply Hello LUANDATO. Let's take a look at your question. We have to find all the prime factors of each option. Option A: $$32=2^5\ \ \ -\ \ \ 48=2^4\cdot3\ \ \ -\ \ \ 52=2^2\cdot13.$$ Option B: $$33=3\cdot11\ \ \ -\ \ \ 42=2\cdot3\cdot7\ \ \ -\ \ \ 56=2^3\cdot7.$$ Option C: $$39=3\cdot13\ \ \ -\ \ \ 40=2^3\cdot5\ \ \ -\ \ \ 54=2\cdot3^3.$$ Option D: $$38=2\cdot19\ \ \ -\ \ \ 49=7^2\ \ \ -\ \ \ 51=3\cdot17.$$ Option E: $$36=2^2\cdot3^2\ \ \ -\ \ \ 42=2\cdot3\cdot7\ \ \ -\ \ \ 56=2^3\cdot7.$$ If we take a look of all distinct prime factors on each set, we can conclude that the option D has 5 distinct prime factors and the rest has 4 distinct prime factors or less. Hence, the correct answer is the option D. I hope this explanation may help you. Feel free to ask me again if you have a doubt. Regards. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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